JEE Mains · Maths · STD 11 - 8. sequence and series
Consider an A.P.: \( a_1, a_{2},....,a_{n} \), \( a_{1}>0 \). If \( a_{2}-a_{1}=\frac{-3}{4} \), \( a_{n}=\frac{1}{4} a_{1} \) and \(\sum_{i=1}^n a_i=\frac{525}{2}\) , then \(\sum_{i=1}^{17} a_i\) is equal to
- A 476
- B 952
- C 238
- D 136
Answer & Solution
Correct Answer
(C) 238
Step-by-step Solution
Detailed explanation
\(S _{ n }=\frac{ n }{2}\left[ a _1+ a _{ n }\right]=\frac{525}{2}, \quad d=\frac{-3}{4}\) \(\frac{ n }{2}\left[ a _1+\frac{ a _1}{4}\right]=\frac{525}{2}\) \(\begin{array}{l}\frac{5 a_1 n}{4}=525 \\ a_1 n=420 \\ a_n=a_1+(n-1)\left(\frac{-3}{4}\right)\end{array}\)…
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